Find all complex number solutions of x^5-1=0

See below.

Step-by-step explanation:

x^5 = 1

x = 1^1/5.

We want the five complex roots of 1:-

Writing in polar form we have:

1 ^ 1/5 =  cos(2πk/5) + isin(2πk/5)

The 5 solutions are found by setting k = 0, 1, 2, 3 and 4.

First one = cos 0 + i sin 0 =  1

Second = cos (2π/5 + isin(2π/5)

= 0.3090 + 0.9511i.

The other 3 can be calculated in the same way.